Abstract
We consider a model for biochemical oxygen demand (BOD) in a semi-infinite river where the BOD is prescribed by a time varying function at the left endpoint. That is, we study the problem with a time varying boundary loading. We obtain the well-posedness for the model when the boundary loading is smooth in time. We also obtain various qualitative results such as ordering, positivity, and boundedness. Of greatest interest, we show that a periodic loading function admits a unique asymptotically attracting periodic solution. For non-smooth loading functions, we obtain weak solutions. Finally, for certain special cases, we show how to obtain explicit solutions in the form of infinite series.
Original language | English (US) |
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Pages (from-to) | 193-221 |
Number of pages | 29 |
Journal | Mathematical Problems in Engineering |
Volume | 5 |
Issue number | 3 |
DOIs | |
State | Published - 1999 |
Externally published | Yes |
Keywords
- Convection-diffusion equations
- Environmental modeling
- Quasi-steady-state
- River model
- Weak solutions
ASJC Scopus subject areas
- General Mathematics
- General Engineering